The aim of the tutorial is to provide an overview on the integration
directions of (exact) Mathematical Programming (MP) techniques, widely used in Operations Research (OR), and Constraint
Programming (CP) for facing Combinatorial Optimization Problems.

The tutorial will start by providing preliminary notions on OR concepts:
we will describe (Mixed) Integer Programming and Linear Programming, their geometrical properties, and solving
algorithms; we will explain how relaxations can be exploited in branch and bound; cutting plane generation techniques
in branch and cut will be presented, and finally column generation approaches for solving large scale problems
are introduced.

In the second part, we focus on how these techniques have been exploited
in CP to enhance its performances. We start from "solver integration" where each solver is in charge
of solving the problem part or abstraction it is more suitable for. Then, we will concentrate on global constraints
as a basis for developing such an integration. We show how to introduce Linear Programming and Cutting Planes techniques
in global constraints, and we provide some examples of their use.

References to recent bibliography are provided. Open problems and research
directions are finally discussed.

In this talk we present some large scale constraint applications which
have been developed at COSYTEC and at IC-Parc/Parc Technologies. We show how the capabilities of the underlying
tools (CHIP and Eclipse) shape the choice of the applications to be considered, and how, at the same time, experience
with applications leads to the further development of the tools. Although CHIP and Eclipse are superficially quite
similar, being constraint systems based on a Prolog kernel, they represent two very different design philosophies.

CHIP is centered on a finite domain solver with powerful, predefined global constraints. Modelling consists in
finding the right combination of these constraints together with a clever search strategy. The typical applications
for this tool are scheduling and resource allocation problems with constraints which are hard to satisfy. As an
example we will discuss one large scale scheduling application for animal feed milling.

Eclipse is using a much faster kernel and enables the programmer to define new constraints and even constraint
solvers quite easily. Modelling here consists in choosing the right hybrid combination of different solving techniques.
This diversity on one side increases the scope of problems that can be tackled, but on the other side also puts
more demands on the programmer. As examples we will discuss two applications currently being developed at Parc
Technologies, one in the airline domain, the other a network optimization problem.